1977, British Journal of Radiology, 50, 769-776
VOLUME 50 NUMBER 599
NOVEMBER 1977
The British Journal of Radiology Measurements of endosteal surface areas in human long bones: relationship to sites of occurrence of osteosarcoma By F. W. Spiers, C.B.E., D.Sc, PhD., F.lnst.P., S. D. King, M.Sc. and A. H. Beddoe, M.Sc, Ph.D., M. Inst. P. University of Leeds, Bone Dosimetry Research, Cookridge Hospital, Leeds LS16 6QB (Receieved May, 1977 and in revised form July, 1977) ABSTRACT
of the six long bones of a male subject aged 50 years (who died from cardiovascular causes without concurrent bone disease) and have attempted to relate our measurements to available data on the distribution of sites of occurrence of sarcoma in long bones. Data on naturally-occurring tumours and on tumours induced by radiation following the skeletal deposition of radium have been studied, our sources being: (a) information published by Thurman et al. (1973) and (b) site and dosimetric data on radium-induced sarcomas of the long bones (33 cases) from the Centre for Human Radiobiology at the Argonne National Laboratory, by the courtesy of Drs. R. E. Rowlands and A. T. Keane. As a result we have been able to examine relationships between tumour appearance and endosteal area and to deduce approximately the relative potential of cortical and trabecular endosteum for tumour initiation.
Using techniques of bone scanning and ashing, the areas of the endosteal surfaces in cortical and trabecular bone have been determined for the proximal, mid and distal thirds of each of the six long bones of an adult human subject. The relative frequency of occurrence of bone sarcomas, scored as to site, has been analysed in relation to these measured areas. Data on tumour occurrence have been drawn from three sources: radium-case data from Rowland and Keane (33 cases), naturally-occurring cases from series by Sissons (139 cases) and by Dahlin (473 cases). A strong correlation is demonstrated between tumour frequency and trabecular area, but correlation with cortical area is poor. By comparing the tumour frequency in the mid thirds of the bones with the total recorded it has been possible to show that the probability of tumour occurrence per unit area of cortical bone, relative to that of trabecular bone, is 0.16 d: 0.06. Analysis of the available dose data for the radium cases shows that in this instance dose has not contributed to the observed correlations. The results lend support to the thesis that tumour occurrence depends on surface area, i.e. on the number of cells at risk.
Evidence presented in a report entitled "The Radio-sensitivity of the Tissues in Bone" (ICRP Report 11,1968) suggests that osteogenic tumours arise in endosteal rather than periosteal tissues, and Vaughan (1970) and Sissons (1970) have concluded that the osteoprogenitor cells, lying close to trabecular surfaces, are the cells most likely to be implicated in tumour initiation. No consideration has so far been given to the relative sensitivity to tumour induction of cortical surfaces compared with trabecular surfaces, except for the suggestion that the osteogenic cells lining Haversian canals and resorption cavities, being less proliferative than those on trabecular surfaces, may on this account be less liable to develop osteogenic sarcoma. The observed paucity of bone tumours in the mid-shafts compared with the ends of long bones gives some support to this suggestion (Thurman et al., 1973). We have therefore measured the absolute areas of endosteal surfaces in the cortical and trabecular bone
MEASUREMENT OF ENDOSTEAL SURFACE AREAS
Areas measured Bone sarcoma in the long bones of the "natural" and the "radium" cases have been scored as occurring respectively in the proximal, mid and distal third of each bone. We have, therefore, determined the surface areas associated with the trabecular and cortical parts of each third of the six long bones of the human subject. In the case of trabecular bone the areas measured are those of the endosteal surfaces associated with marrow cavities. In cortical bone our method includes the areas of the surfaces of the Haversian canals and resorption cavities and also those of the periosteum; the medullary areas are included with the trabecular bone surfaces because they are contiguous with these surfaces. The surfaces included in the trabecular and cortical areas
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FIG. 1. A two-dimensional representation of bone which illustrates the surfaces associated with the two bone types. The cortical surfaces include those of the periosteum (P), Haversian canals (H) and resorption cavities (R); the marrow cavity surfaces include the trabecular (T) and the medullary (M) surfaces.
are illustrated diagrammatically in Fig. 1. The periosteal contribution to the total cortical area is about 19%, but has been included in our calculations because the site scoring of the sarcomas does not differentiate between endosteal and periosteal sites of origin. Our scanning method does not resolve features as small as osteocytes and hence surface areas of lacunae are not included; it is not thought, however, that natural or radiogenic tumours arise from osteocytes (ICRP Report 11,1968). The surface areas were obtained by first determining bone masses and then applying surface to mass ratios measured by a bone-scanning technique. These two parts of the area determination will be considered separately. Determination of bone masses
Each of the bones was divided into three equal lengths and the parts cut longitudinally to give access to the trabeculation and marrow. The bones were weighed prior to and immediately after cutting and then the trabeculation plus marrow was removed, using chisels of suitable curvature. The cortical parts were re-weighed to give directly the weight of cortical bone and by difference the weight of the trabeculation plus marrow that had been removed. Corrections were made for cutting losses; these were negligible for large bones but amounted to 3 to 4% for small bones. An ashing technique was used to determine the mass of trabecular bone that was removed with the
marrow. Essentially the ash weight from the trabeculation plus marrow was compared with the ash weight per gram of a cortical bone specimen from the same bone ashed under identical conditions. The validity of this comparison rests on the assumption that the ratio of the mineral to the organic content of trabecular bone is the same as that of the cortex. All the specimens from a bone were ashed together in unglazed porcelain crucibles in a muffle furnace at approximately 600°C for 24 hours. In order to ash both the trabecular and cortical specimens at the same temperature the combustible fat was first burnt off carefully with a Bunsen flame. Independent determinations of the calcium and phosphorus content of the ash for the trabecular and cortical specimens showed that the organic material had been completely combusted. Determination of surface to mass ratios
For the scanning measurements thin slices were cut from the trabecular and cortical parts of the femur, tibia and humerus. In the case of the trabecular slices allowance was made for this in determining the bone mass by the ashing process; no correction was necessary in determining the cortical mass because the slices were cut after the weighings were completed. Scanning of the trabecular bone was carried out on two or three portions cut from the mid-coronal slices. The soft tissues in the marrow spaces were removed by first flushing the slices with an airpressurized water spray, soaking for two weeks in a weak "biological" detergent at 40°C, and flushing a second time to remove all traces of soft tissue. The cleaned trabecular slices were dried for two days in ethyl alcohol and embedded in a low melting-point metal ("Cerrolow 117") with the aid of a refrigerated centrifuge. Undecalcified sections, 30 ^m thick, were cut from the embedded slices with a Jung K microtome and contact radiographs taken with 10 kV X rays. Frequency distributions of linear path lengths, h through the cavities and t\ through the trabeculae, were measured with an automatic object-plane scanning microscope developed by Darley(1968). If >S is the cavity surface area and V is the volume of the trabeculae then the ratio S/ V can be calculated from the equation SjV=
•
(1)
where E{Ef() is the expectation value of 27/i, the
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i
i
NOVEMBER 1977
Measurements of endosteal surface areas in human long bones
detailed description of the preparation of sections of cortical bone and their measurement has recently i been reported (Beddoe, 1977). trabecular component in a single scan. The evaluaThe calculation of the ratio of surface to volume tion of this equation has been discussed in detail for cortical bone is simplified by the fact that most (Beddoe et al., 1976). It is, however, important to of the canals and cavities are approximately perpenstress that for trabecular bone the surface referred to dicular to the transverse planes for which the pathin Eq. (1) includes both the trabecular surfaces and length distributions are derived. However, because the medullary surface; on the other hand the the medullary surface is included in the marrowdenominator of the ratio only includes the volume of cavity surface in trabecular bone, it is excluded from the trabeculae. Conversion to a surface to mass ratio the calculation of cortical areas. On the assumption has been made using a typical value of bone density that the medullary and periosteal surfaces are of 1.9 g/cm3. approximately equal (Lloyd et al., 1967) the values In the case of cortical bone the sections were of S/ V can be calculated directly from the transverse prepared by hand-grinding thin transverse slices scanning data by the equation (see Beddoe, 1977 and down to a thickness of ~ 8 0 fxm and cleaning by a Beddoe et al, 1976) similar technique to that described above. The sections were then further ground to -—-30 /xm, flushed to remove carborundum particles and dried S/V=• (2) by brief immersion in ethyl alcohol. They were then stained with a modified Van Gieson red stain (Atkinson, 1965) which is particularly suitable where/i' now refers to paths through the mineralized because the photodetector in the scanner is in- component and, as before, fi refers to cavities. Again sensitive to red light. The sections were then the surface to mass ratio is obtained assuming a scanned directly with the bone scanner. A more bone density of 1.9 g/cm3. number of features scanned in a single scan, and where Hfi'ti is the total path length through the
TABLE I Trabecular bone Bone*
Number of tumours
Cortical bone area (m2)
Surface/mass (m2 kg-i)
Area (m2)
Radium cases
Sissons cases
Dahlin cases
Femur
P M D
0.183 0.188 0.185
9.15f 8.43 9.42f
0.408 0.030 0.522
7 0 9
15 3 66
26 29 212
Tibia
P M D
0.151 0.116 0.097
12.1 Of 8.43 8.00f
0.342 0.036 0.126
4 1 2
30 0 5
92 11 12
Fibula
P M D
0.022 0.029 0.027
11.20 8.43 8.71
0.024 0.004 0.029
1 0 0
2 0 0
15 3 1
Humerus
P M D
0.082 0.089 0.125
12.48f 8.43 8.71
0.187 0.014 0.027
4 1 0
13 1 2
55 4 5
Radius
P M D
0.034 0.026 0.025
11.20 8.43 8.71
0.052 0.006 0.024
2.5 0 0
0 0 1
1 0 4
Ulna
P M D
0.076 0.040 0.027
11.20 8.43 8.71
0.105 0.013 0.022
1.5 0 0
1 0 0
1 0 2
139
473
Totals * Notation: P=proximal, M = m i d and D = distal third of bones. t Measured values of surface to mass ratio; for source of other values see text.
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50, No. 599 F. W. Spiers, S. D. King and A. H. Beddoe RESULTS
Cortical and Trabecular Surface Areas The surface areas of the cortical and trabecular parts of each third of the six long bones are given in columns 2 and 4 of Table I. The surface to mass ratio for cortical bone has been taken as 1.57 m2/kg which is the mean, weighted by cortical mass, of values measured for the femur, tibia and humerus.
•2 -3 TRAKCUIAR AREA (m 1 )
FIG. 2. Radium-case data; numbers of tumours versus measured trabecular area. Note that there are points of zero tumour incidence (8 in all, see Table I) 2below a trabecular area of 0.03 m .
The corresponding ratios for the trabecular bone sections have been obtained as follows: (1) by scanning of the bone sections themselves (femur P, tibia P, humerus P, femur D, tibia D), (2) by applying the corresponding averages of these measured values in the case of the proximal and distal sections of the other bones and (3) by using a common value for the mid sections taken to be the same as that for trabeculation of similar appearance in the neck of the femur. It may be noted that directly measured surface/mass ratios have been used for the sections having large surface areas. The numbers of bone sarcoma scored as occurring in the proximal, mid and distal thirds are also given in the last three columns of Table I for the radium case data (column 5) and for the naturally-occurring tumours listed by Sissons and by Dahlin (taken from Thurman et al., 1973) in columns 6 and 7 respectively. For the radium-case data and Dahlin's data, all the reported tumours have been assigned respectively to the relevant bone sections; for Sissons' data, only 139 sarcoma out of a total of 204 long bone tumours have been scored and the numbers given in Table I refer only to these cases. Radium case data: relationship to trabecular and cortical surface areas The 33 bone tumours in Table I includes 23 osteogenic sarcomas, nine fibrosarcomas and one spindle-cell sarcoma. The numbers of tumours scored for each bone section are plotted against the trabecular surface area of the section in Fig. 2, from
TABLE II LINEAR REGRESSION CONTANTS AND CORRELATION COEFFICIENTS
Data
Gradient ±SE (areas in m2)
Constant
Correlation coefficient
1. Radium case data Tumour numbers versus trabecular area. 2. Radium case data Tumour numbers versus cortical area.
16.3±1.2
0.05
0.962
27.6 ±8.5
-0.46
0.630
Percentage tumour occurrence versus trabecular area. 3. Sissons' data 4. Dahlin's data 5. Radium case data
68.4±8.5 59.2±7.7 49.3 ±3.5
-1.94 -0.95 0.16
0.896 0.836 0.962
Percentage tumour occurrence in whole bones versus trabecular area. 6. Sissons' data 7. Dahlin's data 8. Radium case data
66.9±3.8 60.8 ±4.8 48.0 ±4.4
-5.31 -3.37 0.93
0.994 0.988 0.983
1.07
0.893
9. Radium case data Tumour number versus trabecular area X absorbed dose to skeleton
0.172 772
±0.031
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1977
Measurements of endosteal surface areas in human long bones 60
5 S4
CORTICAL AREA (m 3 )
•Hm
05
»Tm
10 CORTICAL
FIG. 5. Percentage tumour occurrence versus measured cortical area; data from Sissons (A)> Dahlin ( • ) and the radiumcase data ( 9 ) . 15
-20
AREA (m 1 )
3. Radium-case data; numbers of tumours versus measured cortical area. FIG.
•2 -3 -4 TRABECULAR AREA(m*)
FIG. 4. Percentage tumour occurrence versus measured trabecular area; data from Sissons (S, ^ ) , Dahlin (D, • ) and the radium-cases (R, £ ) .
which it is evident that tumour number is approximately linearly related to trabecular area. The linear regression line in Fig. 2 has been fitted by the method of least squares with the constants as given in entry 1 of Table II. A high correlation coefficient of 0.962 is obtained. A plot of tumour numbers against the cortical surface area for each section is shown in Fig. 3. Here the correlation is very poor, with a correlation coefficient for linear regression of only 0.630. Admittedly the regression is steeper than in the case of trabecular bone, but this stems from the fact that the
larger tumour numbers occur at the proximal and distal ends of the bones where the cortical areas are less than the trabecular areas. On the other hand few tumours occur in the mid thirds where the cortical areas are much greater than the trabecular areas. Poor correlation is illustrated, for example, in the data for the femur where tumour numbers are recorded as 7, 0 and 9 for the proximal, mid and distal thirds, where the cortical areas are almost equal with values of 0.183, 0.188 and 0.185 m2 respectively. Comparison of data for natural and radium-induced tumours All the data for natural and radium-induced tumours given in Table I have been plotted as percentage tumour incidence against the trabecular surface area of each section in Fig. 4. Correlation with trabecular surface area is not as good as in the radium-case data and some differences appears between the three sets of data. Nevertheless the concordance between the data still suggests that tumour occurrence correlates with trabecular surface area as shown by the relatively good correlation coefficients in Table II (entries 3, 4 and 5). The plot of the same data against cortical surface area in Fig. 5 shows a similarly poor correlation to that exhibited for the radium cases in Fig. 3. Indeed, for the femur nine points lying between 0 and 47 % tumour occurrence are recorded for cortical areas in the narrow range 0.183 to 0.188 m2. The total percentage tumour occurrence for each long bone is shown in Fig. 6 plotted against the total trabecular area for each bone. Improved statistics are now obtained and a closer definition of the regression lines. The data for the natural tumours
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2 4 6 8 MEAN SKELETAL DOSE x TRABECULAR AREA (krod.m 2 ) •2
-4 -6 -8 TOTAL TRABECULAR AREA FOR EACH BONE ( M 2 )
FIG. 6. Percentage tumour occurrence in whole hones versus trabecular area; data from Sissons (S, A), Dahlin (D, • ) and the radium-case data (R, %i).
FIG. 8. Radium-case data; numbers of tumours recorded for each interval of 0.2 krad m2 of the parameter "mean skeletal dose X trabecular area".
retained a-particle energy divided by the bone mass (5000 g). The tumour numbers, as scored in thirds in Fig. 2, have been replotted in Fig. 7 against the mean skeletal dose for each group of tumours; the range of the average skeletal dose in each group is also shown. Clearly there is no correlation between the numbers of tumours (for a given trabecular area) and the average skeletal dose, although it should be noted that data on the a-particle dose to the relevant soft tissue in the bones is unknown and probably Rp £7~ unobtainable. Up Rp r Nevertheless two further analyses have been m S 10 15 20 attempted using a new dose parameter, calculated as MEAN ABSORBED DOSE TO SKELETON (krad) "average skeletal dose X trabecular area". In the FIG. 7. last entry in Table II the regression is calculated for Radium-case data; numbers of tumours scored in each third the number of tumours scored in each bone section of each bone versus mean absorbed dose to the skeleton; against the average value of the "dose X area" horizontal bars indicate the ranges of doses recorded. parameter for that section. As might be expected from Sissons and Dahlin lie close together with the from Figs. 2 and 7, the correlation coefficient is radium-case data lying on a regression line of lower lowered, not raised, by the inclusion of dose in the slope. The correlation coefficients (Table II entries parameter tested. In the second analysis the average skeletal dose X area parameter has been calculated 6, 7 and 8) are uniformly high. for each tumour and the numbers of tumours 2 Consideration of a-particle dose in the radium-case data counted in intervals of 0.2 krad m . The results are 226 Not all the radium-case data relate to pure Ra shown in Fig. 8 from which little correlation is with irradiations. In the case of 18 recorded tumours evident, except possibly a linear rise of tumours 2 226 Ra and its daughter products were either the sole the dose X area parameter up to 0.6 krad m . Clearly or principal irradiators, in 12 cases the irradiation the greatest caution must be exercised in examining was principally by 228Ra and its daughters although these results both because the tumour numbers are some 226Ra was also present, while in three cases the so small and also because the doses are all in excess of irradiation was contributed almost equally by the 3 krads for2 points beyond a dose X area parameter of two radionuclides. Measured 226Ra burdens, meas- 1 krad m , and these accumulated doses may be too ured 228 Ra/ 226 Ra ratios and the calculated average high to reflect a dose-response relationship. It skeletal absorbed dose to the year of diagnosis are appears that the strongest influence on tumour known for all the cases (Rowland and Keane, 1976); incidence in these cases lies in the area of trabecular the average skeletal absorbed dose is taken as the surface at risk. (T
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Measurements of endosteal surface areas in human long bones TABLE III PROBABILITY OF BONE TUMOUR
RELATIVE OCCURRENCE PER UNIT AREA OF CORTICAL AND TRABECULAR ENDOSTEUM
SUMMATION OF ENDOSTEAL AREAS AND OF TUMOUR NUMBERS
The data examined above can be used to estimate the relative probability of bone tumour occurrence in cortical and trabecular bone. It is evident from Table I that the number of tumours appearing in the mid-thirds of the long bones is small compared with the number in the outer thirds, corresponding in general to the small fraction of the trabecular area associated with the mid-thirds. On the other hand, for each bone, the cortical area is roughly the same for all three parts of the bone. These features and the degree of correlation between tumour occurrence and trabecular area suggest that the cortical endosteum has a considerably lower potential for tumour appearance per unit area than trabecular endosteum. Although the radium-case data and that for the natural tumours are not identical in all respects (e.g. some differences in the slopes of the regression lines in Figs. 4 and 6 are evident), there are no systematic differences in the fractions of the total tumours appearing in the mid-thirds; the fraction for the radium-case data lies between the values for the two natural tumour series, but the actual numbers are small. The data for the three series are therefore pooled to obtain the number of tumours appearing in the mid-thirds compared with the total tumours scored. The data are presented in Table III together with the corresponding areas of the cortical and trabecular endosteum; standard errors are given for each summed area based on an estimated error of ± 5 % for each individual area measurement. If we assume that the probability of tumour occurrence per unit area (m2) of endosteum is PQ and PT respectively for cortical and trabecular bone and use the areas given in Table III, we can equate a calculated ratio of probabilities of tumour occurrence, mid-thirds/total, to the observed ratio of the corresponding tumour numbers, 53/645; i.e. we can write: tumours in mid-thirds total tumours
0.488 P c +0.103 P T
1.522Pc+1.97lPT _53_ 645
which gives :P c /P T =0.163 ±0.060 (SE).
(3) (4)
where the standard error includes the errors given in Table III and a statistical error on the numbers of tumours scored. The order of accuracy of this value of P C / P T can be established in another way. We can assign various values to PC/PT between 0 (where no
Areas summed
Cortical endosteum (m2)
Trabecular endosteum (m2)
Numbers of tumours
Totals for six long bones Totals for mid-sections
1.522±.022
1.971 ±.040
645
O.488±.OI2
0.103 ±.003
53
068
FIG. 9. Cortical correlation coefficients versus assigned values of PC/PT; the correlation coefficients are for linear regression of numbers of tumours apportioned to cortical bone in individual thirds against the corresponding cortical area.
tumours would occur in the cortex) to 1.0 where the cortical and trabecular surfaces would be equally sensitive. Using any one of these values and the individual values of the cortical and trabecular surface areas, the observed tumour numbers for a bone section can be apportioned between the cortex and the trabeculation of that section. The apportioned numbers for cortical bone can then be tested for correlation with cortical area and the correlation coefficient for linear regression calculated. These correlation coefficients are shown in Fig. 9, plotted against the assigned values of PC/PT- The correlation coefficient shows a maximum at P C / P T ^0.2, thus lending support to the value of PC/PT calculated by Equation (4). DISCUSSION AND CONCLUSIONS
The correlations shown in Table II and in Figs. 2, 4 and 6 suggest that in the case of the human long bones the occurrence of bone tumours shows an approximately linear relationship with trabecular surface area. This is an example that lends some
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quantitative support to the hypothesis that, under given circumstances, tumour induction is proportional to the number of cells at risk (Mayneord and Clarke, 1975). It does not follow that similar correlations can be assumed for other bones in the skeleton; the data given by Thurman et ah, (1973) suggest that this may be difficult, but as yet knowledge of the surface areas involved is not available to examine the question. Among the long bones themselves there are some discrepencies in that, for the natural tumours, more occur in the distal femur and less in the proximal femur than the regression lines suggest, whereas the corresponding points for the radium-case data fit quite well. The slopes of the regression lines are also somewhat different for the two sets of natural tumour data and both differ from that obtained for the radium cases. Nevertheless there is still a strong suggestion of a relationship between the frequency of occurrence at a given site and the associated surface area. As to other possible factors that might influence the location of bone tumours, there appear to be no data reported on variation with age or sex. The known greater proliferative capacity of cells near trabecular surfaces presumably underlies the greater rate of bone turnover in trabecular compared with cortical bone, and our results are in accord with this. With regard to the radium-case data, the analyses against skeletal dose have been examined as far as present data will allow. The two main features of the dose data are (a) the great diversity of dose among the cases examined and (b) the very high doses sustained in the majority of the cases. Under these circumstances it is evident that area of surface at risk is a stronger factor than dose in influencing the site of tumour appearance. Assuming, however, that radiation is the causative agent in these radium cases, a very approximate estimate can be made of the sarcoma risk per unit area of endosteal surface under conditions of very high skeletal dose. If the 33 longbone sarcomas listed in Table I are taken as occurring in the 777 cases analysed by Rowland et al. (1970), the risk per unit area of trabecular surface is about 2 X 10~6 cm"2 over a period of 40 to 50 years of observation, the risk to surfaces in cortical bone being about six times lower. If the cells at risk lie within about 10 /xm of the surfaces, the probability of tumour occurrence in the trabeculation of the long bones would thus be about 2 X 10~9 per g of cells. These estimates can only be approximate because the tracing of radium cases is incomplete. Considering all the data together it has been possible to derive a value for the relative probability
of tumour occurrence per unit area of cortical and trabecular endosteum. The value obtained gives a quantitative figure which supports the qualitative expectations based on biological considerations and the practical observation that comparatively few tumours appear in the mid thirds of the long bones. A value of P C / P T = 0 . 1 6 is suggested as a reasonable value to use in any dosimetric calculation of carcinogenic risk to cortical bone surfaces compared with that to trabecular surfaces. ACKNO WLEDGMENTS
We are greatly indebted to many people with whom we have discussed various aspects of this work, particularly in the early stages with Dr. C. W. Mays of the University of Utah and Dr. J. H. Marshall of the Argonne National Laboratory and later with Dame Janet Vaughan, Sir Edward Pochin and Professor W. V. Mayneord. Our thanks are also due to Drs. R. E. Rowland and A. T. Keane of the Argonne National Laboratory for data on the radium cases. We gratefully acknowledge the help of Dr. W. K. J. Walls of the Department of Anatomy, Leeds University and the technical help of Miss Barbara Prestwich. The work was supported by the Medical Research Council. REFERENCES ATKINSON, P. J., 1965. Changes in resorption spaces in femoral cortical bone with age. Journal of Pathology and Bacteriology, 89,173-178. BEDDOE, A. H., 1977. Measurements of the microscopic structure of cortical bone. Physics in Medicine and Biologv, 22, 298-308. BEDDOE, A. H., DARLEY, P. J., and SPIERS, F. W., 1976.
Measurements of trabecular bone structure in man. Physics in Medicine and Biology, 21, 589-607. DARLEY, P. J., 1968. Measurement of linear path length distributions in bone and bone marrow using a scanning technique. In Proceedings of a Symposium on Microdosimetry, Ispra, Italy, E.A.E.C. Report E.U.R. d-f-e-, pp.509-526. International Commission on Radiological Protection, 1968. A Review of the radiosensitivity of the tissues in bone. I.C.R.P. Publication No. 11 (Pergamon Press, Oxford). LLOYD, E., ROWLAND, R. E., HODGES, D., and MARSHALL,
J. H., 1967. Surface/volume ratios of bone determined by computer analysis of micro-radiographs. Argonne National Laboratory, Radiological Physics Division Report ANL7360, pp. 93-96. MAYNEORD, W. V., and CLARKE, R. H., 1975. Carcinogenesis
and radiation risk. A biomathematical reconnaissance. British Journal of Radiology, Supplement 12, Chapter 1. ROWLAND, R. E., FAILLA, P. M., KEANE, A. T., and STEHNEY
A. F., 1970. Some dose-response relationships for tumour incidence in radium patients. Argonne National Laboratory Report ANL-7760II, pp. 1-17. ROWLAND, R. E., and KEANE, A. T., 1976. Personal com-
munication. SISSONS, H. A., 1970. Dimensions of cells covering bone surfaces. Medical Research Council (London) SubCommittee on Permissible Levels, PIRC/PL/70/4. THURMAN, G. B., MAYS, C. W., TAYLOR, S. N., KEANE,
A. T., and SISSONS, H. A., 1973. Skeletal location of radiation-induced and naturally occurring osteosarcomas in man and dog. Cancer Research, 33,1604—1607. VAUGHAN, J., 1970. Note on character of cells on trabecular bone surfaces in adult human vertebrae. Medical Research Council (London) Sub-Committee on Permissible Levels, PIRC/PL/ 70/1.
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VOLUME 50 NUMBER 599
NOVEMBER 1977
The British Journal of Radiology Measurements of endosteal surface areas in human long bones: relationship to sites of occurrence of osteosarcoma By F. W. Spiers, C.B.E., D.Sc, PhD., F.lnst.P., S. D. King, M.Sc. and A. H. Beddoe, M.Sc, Ph.D., M. Inst. P. University of Leeds, Bone Dosimetry Research, Cookridge Hospital, Leeds LS16 6QB (Receieved May, 1977 and in revised form July, 1977) ABSTRACT
of the six long bones of a male subject aged 50 years (who died from cardiovascular causes without concurrent bone disease) and have attempted to relate our measurements to available data on the distribution of sites of occurrence of sarcoma in long bones. Data on naturally-occurring tumours and on tumours induced by radiation following the skeletal deposition of radium have been studied, our sources being: (a) information published by Thurman et al. (1973) and (b) site and dosimetric data on radium-induced sarcomas of the long bones (33 cases) from the Centre for Human Radiobiology at the Argonne National Laboratory, by the courtesy of Drs. R. E. Rowlands and A. T. Keane. As a result we have been able to examine relationships between tumour appearance and endosteal area and to deduce approximately the relative potential of cortical and trabecular endosteum for tumour initiation.
Using techniques of bone scanning and ashing, the areas of the endosteal surfaces in cortical and trabecular bone have been determined for the proximal, mid and distal thirds of each of the six long bones of an adult human subject. The relative frequency of occurrence of bone sarcomas, scored as to site, has been analysed in relation to these measured areas. Data on tumour occurrence have been drawn from three sources: radium-case data from Rowland and Keane (33 cases), naturally-occurring cases from series by Sissons (139 cases) and by Dahlin (473 cases). A strong correlation is demonstrated between tumour frequency and trabecular area, but correlation with cortical area is poor. By comparing the tumour frequency in the mid thirds of the bones with the total recorded it has been possible to show that the probability of tumour occurrence per unit area of cortical bone, relative to that of trabecular bone, is 0.16 d: 0.06. Analysis of the available dose data for the radium cases shows that in this instance dose has not contributed to the observed correlations. The results lend support to the thesis that tumour occurrence depends on surface area, i.e. on the number of cells at risk.
Evidence presented in a report entitled "The Radio-sensitivity of the Tissues in Bone" (ICRP Report 11,1968) suggests that osteogenic tumours arise in endosteal rather than periosteal tissues, and Vaughan (1970) and Sissons (1970) have concluded that the osteoprogenitor cells, lying close to trabecular surfaces, are the cells most likely to be implicated in tumour initiation. No consideration has so far been given to the relative sensitivity to tumour induction of cortical surfaces compared with trabecular surfaces, except for the suggestion that the osteogenic cells lining Haversian canals and resorption cavities, being less proliferative than those on trabecular surfaces, may on this account be less liable to develop osteogenic sarcoma. The observed paucity of bone tumours in the mid-shafts compared with the ends of long bones gives some support to this suggestion (Thurman et al., 1973). We have therefore measured the absolute areas of endosteal surfaces in the cortical and trabecular bone
MEASUREMENT OF ENDOSTEAL SURFACE AREAS
Areas measured Bone sarcoma in the long bones of the "natural" and the "radium" cases have been scored as occurring respectively in the proximal, mid and distal third of each bone. We have, therefore, determined the surface areas associated with the trabecular and cortical parts of each third of the six long bones of the human subject. In the case of trabecular bone the areas measured are those of the endosteal surfaces associated with marrow cavities. In cortical bone our method includes the areas of the surfaces of the Haversian canals and resorption cavities and also those of the periosteum; the medullary areas are included with the trabecular bone surfaces because they are contiguous with these surfaces. The surfaces included in the trabecular and cortical areas
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FIG. 1. A two-dimensional representation of bone which illustrates the surfaces associated with the two bone types. The cortical surfaces include those of the periosteum (P), Haversian canals (H) and resorption cavities (R); the marrow cavity surfaces include the trabecular (T) and the medullary (M) surfaces.
are illustrated diagrammatically in Fig. 1. The periosteal contribution to the total cortical area is about 19%, but has been included in our calculations because the site scoring of the sarcomas does not differentiate between endosteal and periosteal sites of origin. Our scanning method does not resolve features as small as osteocytes and hence surface areas of lacunae are not included; it is not thought, however, that natural or radiogenic tumours arise from osteocytes (ICRP Report 11,1968). The surface areas were obtained by first determining bone masses and then applying surface to mass ratios measured by a bone-scanning technique. These two parts of the area determination will be considered separately. Determination of bone masses
Each of the bones was divided into three equal lengths and the parts cut longitudinally to give access to the trabeculation and marrow. The bones were weighed prior to and immediately after cutting and then the trabeculation plus marrow was removed, using chisels of suitable curvature. The cortical parts were re-weighed to give directly the weight of cortical bone and by difference the weight of the trabeculation plus marrow that had been removed. Corrections were made for cutting losses; these were negligible for large bones but amounted to 3 to 4% for small bones. An ashing technique was used to determine the mass of trabecular bone that was removed with the
marrow. Essentially the ash weight from the trabeculation plus marrow was compared with the ash weight per gram of a cortical bone specimen from the same bone ashed under identical conditions. The validity of this comparison rests on the assumption that the ratio of the mineral to the organic content of trabecular bone is the same as that of the cortex. All the specimens from a bone were ashed together in unglazed porcelain crucibles in a muffle furnace at approximately 600°C for 24 hours. In order to ash both the trabecular and cortical specimens at the same temperature the combustible fat was first burnt off carefully with a Bunsen flame. Independent determinations of the calcium and phosphorus content of the ash for the trabecular and cortical specimens showed that the organic material had been completely combusted. Determination of surface to mass ratios
For the scanning measurements thin slices were cut from the trabecular and cortical parts of the femur, tibia and humerus. In the case of the trabecular slices allowance was made for this in determining the bone mass by the ashing process; no correction was necessary in determining the cortical mass because the slices were cut after the weighings were completed. Scanning of the trabecular bone was carried out on two or three portions cut from the mid-coronal slices. The soft tissues in the marrow spaces were removed by first flushing the slices with an airpressurized water spray, soaking for two weeks in a weak "biological" detergent at 40°C, and flushing a second time to remove all traces of soft tissue. The cleaned trabecular slices were dried for two days in ethyl alcohol and embedded in a low melting-point metal ("Cerrolow 117") with the aid of a refrigerated centrifuge. Undecalcified sections, 30 ^m thick, were cut from the embedded slices with a Jung K microtome and contact radiographs taken with 10 kV X rays. Frequency distributions of linear path lengths, h through the cavities and t\ through the trabeculae, were measured with an automatic object-plane scanning microscope developed by Darley(1968). If >S is the cavity surface area and V is the volume of the trabeculae then the ratio S/ V can be calculated from the equation SjV=
•
(1)
where E{Ef() is the expectation value of 27/i, the
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i
i
NOVEMBER 1977
Measurements of endosteal surface areas in human long bones
detailed description of the preparation of sections of cortical bone and their measurement has recently i been reported (Beddoe, 1977). trabecular component in a single scan. The evaluaThe calculation of the ratio of surface to volume tion of this equation has been discussed in detail for cortical bone is simplified by the fact that most (Beddoe et al., 1976). It is, however, important to of the canals and cavities are approximately perpenstress that for trabecular bone the surface referred to dicular to the transverse planes for which the pathin Eq. (1) includes both the trabecular surfaces and length distributions are derived. However, because the medullary surface; on the other hand the the medullary surface is included in the marrowdenominator of the ratio only includes the volume of cavity surface in trabecular bone, it is excluded from the trabeculae. Conversion to a surface to mass ratio the calculation of cortical areas. On the assumption has been made using a typical value of bone density that the medullary and periosteal surfaces are of 1.9 g/cm3. approximately equal (Lloyd et al., 1967) the values In the case of cortical bone the sections were of S/ V can be calculated directly from the transverse prepared by hand-grinding thin transverse slices scanning data by the equation (see Beddoe, 1977 and down to a thickness of ~ 8 0 fxm and cleaning by a Beddoe et al, 1976) similar technique to that described above. The sections were then further ground to -—-30 /xm, flushed to remove carborundum particles and dried S/V=• (2) by brief immersion in ethyl alcohol. They were then stained with a modified Van Gieson red stain (Atkinson, 1965) which is particularly suitable where/i' now refers to paths through the mineralized because the photodetector in the scanner is in- component and, as before, fi refers to cavities. Again sensitive to red light. The sections were then the surface to mass ratio is obtained assuming a scanned directly with the bone scanner. A more bone density of 1.9 g/cm3. number of features scanned in a single scan, and where Hfi'ti is the total path length through the
TABLE I Trabecular bone Bone*
Number of tumours
Cortical bone area (m2)
Surface/mass (m2 kg-i)
Area (m2)
Radium cases
Sissons cases
Dahlin cases
Femur
P M D
0.183 0.188 0.185
9.15f 8.43 9.42f
0.408 0.030 0.522
7 0 9
15 3 66
26 29 212
Tibia
P M D
0.151 0.116 0.097
12.1 Of 8.43 8.00f
0.342 0.036 0.126
4 1 2
30 0 5
92 11 12
Fibula
P M D
0.022 0.029 0.027
11.20 8.43 8.71
0.024 0.004 0.029
1 0 0
2 0 0
15 3 1
Humerus
P M D
0.082 0.089 0.125
12.48f 8.43 8.71
0.187 0.014 0.027
4 1 0
13 1 2
55 4 5
Radius
P M D
0.034 0.026 0.025
11.20 8.43 8.71
0.052 0.006 0.024
2.5 0 0
0 0 1
1 0 4
Ulna
P M D
0.076 0.040 0.027
11.20 8.43 8.71
0.105 0.013 0.022
1.5 0 0
1 0 0
1 0 2
139
473
Totals * Notation: P=proximal, M = m i d and D = distal third of bones. t Measured values of surface to mass ratio; for source of other values see text.
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33
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50, No. 599 F. W. Spiers, S. D. King and A. H. Beddoe RESULTS
Cortical and Trabecular Surface Areas The surface areas of the cortical and trabecular parts of each third of the six long bones are given in columns 2 and 4 of Table I. The surface to mass ratio for cortical bone has been taken as 1.57 m2/kg which is the mean, weighted by cortical mass, of values measured for the femur, tibia and humerus.
•2 -3 TRAKCUIAR AREA (m 1 )
FIG. 2. Radium-case data; numbers of tumours versus measured trabecular area. Note that there are points of zero tumour incidence (8 in all, see Table I) 2below a trabecular area of 0.03 m .
The corresponding ratios for the trabecular bone sections have been obtained as follows: (1) by scanning of the bone sections themselves (femur P, tibia P, humerus P, femur D, tibia D), (2) by applying the corresponding averages of these measured values in the case of the proximal and distal sections of the other bones and (3) by using a common value for the mid sections taken to be the same as that for trabeculation of similar appearance in the neck of the femur. It may be noted that directly measured surface/mass ratios have been used for the sections having large surface areas. The numbers of bone sarcoma scored as occurring in the proximal, mid and distal thirds are also given in the last three columns of Table I for the radium case data (column 5) and for the naturally-occurring tumours listed by Sissons and by Dahlin (taken from Thurman et al., 1973) in columns 6 and 7 respectively. For the radium-case data and Dahlin's data, all the reported tumours have been assigned respectively to the relevant bone sections; for Sissons' data, only 139 sarcoma out of a total of 204 long bone tumours have been scored and the numbers given in Table I refer only to these cases. Radium case data: relationship to trabecular and cortical surface areas The 33 bone tumours in Table I includes 23 osteogenic sarcomas, nine fibrosarcomas and one spindle-cell sarcoma. The numbers of tumours scored for each bone section are plotted against the trabecular surface area of the section in Fig. 2, from
TABLE II LINEAR REGRESSION CONTANTS AND CORRELATION COEFFICIENTS
Data
Gradient ±SE (areas in m2)
Constant
Correlation coefficient
1. Radium case data Tumour numbers versus trabecular area. 2. Radium case data Tumour numbers versus cortical area.
16.3±1.2
0.05
0.962
27.6 ±8.5
-0.46
0.630
Percentage tumour occurrence versus trabecular area. 3. Sissons' data 4. Dahlin's data 5. Radium case data
68.4±8.5 59.2±7.7 49.3 ±3.5
-1.94 -0.95 0.16
0.896 0.836 0.962
Percentage tumour occurrence in whole bones versus trabecular area. 6. Sissons' data 7. Dahlin's data 8. Radium case data
66.9±3.8 60.8 ±4.8 48.0 ±4.4
-5.31 -3.37 0.93
0.994 0.988 0.983
1.07
0.893
9. Radium case data Tumour number versus trabecular area X absorbed dose to skeleton
0.172 772
±0.031
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1977
Measurements of endosteal surface areas in human long bones 60
5 S4
CORTICAL AREA (m 3 )
•Hm
05
»Tm
10 CORTICAL
FIG. 5. Percentage tumour occurrence versus measured cortical area; data from Sissons (A)> Dahlin ( • ) and the radiumcase data ( 9 ) . 15
-20
AREA (m 1 )
3. Radium-case data; numbers of tumours versus measured cortical area. FIG.
•2 -3 -4 TRABECULAR AREA(m*)
FIG. 4. Percentage tumour occurrence versus measured trabecular area; data from Sissons (S, ^ ) , Dahlin (D, • ) and the radium-cases (R, £ ) .
which it is evident that tumour number is approximately linearly related to trabecular area. The linear regression line in Fig. 2 has been fitted by the method of least squares with the constants as given in entry 1 of Table II. A high correlation coefficient of 0.962 is obtained. A plot of tumour numbers against the cortical surface area for each section is shown in Fig. 3. Here the correlation is very poor, with a correlation coefficient for linear regression of only 0.630. Admittedly the regression is steeper than in the case of trabecular bone, but this stems from the fact that the
larger tumour numbers occur at the proximal and distal ends of the bones where the cortical areas are less than the trabecular areas. On the other hand few tumours occur in the mid thirds where the cortical areas are much greater than the trabecular areas. Poor correlation is illustrated, for example, in the data for the femur where tumour numbers are recorded as 7, 0 and 9 for the proximal, mid and distal thirds, where the cortical areas are almost equal with values of 0.183, 0.188 and 0.185 m2 respectively. Comparison of data for natural and radium-induced tumours All the data for natural and radium-induced tumours given in Table I have been plotted as percentage tumour incidence against the trabecular surface area of each section in Fig. 4. Correlation with trabecular surface area is not as good as in the radium-case data and some differences appears between the three sets of data. Nevertheless the concordance between the data still suggests that tumour occurrence correlates with trabecular surface area as shown by the relatively good correlation coefficients in Table II (entries 3, 4 and 5). The plot of the same data against cortical surface area in Fig. 5 shows a similarly poor correlation to that exhibited for the radium cases in Fig. 3. Indeed, for the femur nine points lying between 0 and 47 % tumour occurrence are recorded for cortical areas in the narrow range 0.183 to 0.188 m2. The total percentage tumour occurrence for each long bone is shown in Fig. 6 plotted against the total trabecular area for each bone. Improved statistics are now obtained and a closer definition of the regression lines. The data for the natural tumours
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2 4 6 8 MEAN SKELETAL DOSE x TRABECULAR AREA (krod.m 2 ) •2
-4 -6 -8 TOTAL TRABECULAR AREA FOR EACH BONE ( M 2 )
FIG. 6. Percentage tumour occurrence in whole hones versus trabecular area; data from Sissons (S, A), Dahlin (D, • ) and the radium-case data (R, %i).
FIG. 8. Radium-case data; numbers of tumours recorded for each interval of 0.2 krad m2 of the parameter "mean skeletal dose X trabecular area".
retained a-particle energy divided by the bone mass (5000 g). The tumour numbers, as scored in thirds in Fig. 2, have been replotted in Fig. 7 against the mean skeletal dose for each group of tumours; the range of the average skeletal dose in each group is also shown. Clearly there is no correlation between the numbers of tumours (for a given trabecular area) and the average skeletal dose, although it should be noted that data on the a-particle dose to the relevant soft tissue in the bones is unknown and probably Rp £7~ unobtainable. Up Rp r Nevertheless two further analyses have been m S 10 15 20 attempted using a new dose parameter, calculated as MEAN ABSORBED DOSE TO SKELETON (krad) "average skeletal dose X trabecular area". In the FIG. 7. last entry in Table II the regression is calculated for Radium-case data; numbers of tumours scored in each third the number of tumours scored in each bone section of each bone versus mean absorbed dose to the skeleton; against the average value of the "dose X area" horizontal bars indicate the ranges of doses recorded. parameter for that section. As might be expected from Sissons and Dahlin lie close together with the from Figs. 2 and 7, the correlation coefficient is radium-case data lying on a regression line of lower lowered, not raised, by the inclusion of dose in the slope. The correlation coefficients (Table II entries parameter tested. In the second analysis the average skeletal dose X area parameter has been calculated 6, 7 and 8) are uniformly high. for each tumour and the numbers of tumours 2 Consideration of a-particle dose in the radium-case data counted in intervals of 0.2 krad m . The results are 226 Not all the radium-case data relate to pure Ra shown in Fig. 8 from which little correlation is with irradiations. In the case of 18 recorded tumours evident, except possibly a linear rise of tumours 2 226 Ra and its daughter products were either the sole the dose X area parameter up to 0.6 krad m . Clearly or principal irradiators, in 12 cases the irradiation the greatest caution must be exercised in examining was principally by 228Ra and its daughters although these results both because the tumour numbers are some 226Ra was also present, while in three cases the so small and also because the doses are all in excess of irradiation was contributed almost equally by the 3 krads for2 points beyond a dose X area parameter of two radionuclides. Measured 226Ra burdens, meas- 1 krad m , and these accumulated doses may be too ured 228 Ra/ 226 Ra ratios and the calculated average high to reflect a dose-response relationship. It skeletal absorbed dose to the year of diagnosis are appears that the strongest influence on tumour known for all the cases (Rowland and Keane, 1976); incidence in these cases lies in the area of trabecular the average skeletal absorbed dose is taken as the surface at risk. (T
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Measurements of endosteal surface areas in human long bones TABLE III PROBABILITY OF BONE TUMOUR
RELATIVE OCCURRENCE PER UNIT AREA OF CORTICAL AND TRABECULAR ENDOSTEUM
SUMMATION OF ENDOSTEAL AREAS AND OF TUMOUR NUMBERS
The data examined above can be used to estimate the relative probability of bone tumour occurrence in cortical and trabecular bone. It is evident from Table I that the number of tumours appearing in the mid-thirds of the long bones is small compared with the number in the outer thirds, corresponding in general to the small fraction of the trabecular area associated with the mid-thirds. On the other hand, for each bone, the cortical area is roughly the same for all three parts of the bone. These features and the degree of correlation between tumour occurrence and trabecular area suggest that the cortical endosteum has a considerably lower potential for tumour appearance per unit area than trabecular endosteum. Although the radium-case data and that for the natural tumours are not identical in all respects (e.g. some differences in the slopes of the regression lines in Figs. 4 and 6 are evident), there are no systematic differences in the fractions of the total tumours appearing in the mid-thirds; the fraction for the radium-case data lies between the values for the two natural tumour series, but the actual numbers are small. The data for the three series are therefore pooled to obtain the number of tumours appearing in the mid-thirds compared with the total tumours scored. The data are presented in Table III together with the corresponding areas of the cortical and trabecular endosteum; standard errors are given for each summed area based on an estimated error of ± 5 % for each individual area measurement. If we assume that the probability of tumour occurrence per unit area (m2) of endosteum is PQ and PT respectively for cortical and trabecular bone and use the areas given in Table III, we can equate a calculated ratio of probabilities of tumour occurrence, mid-thirds/total, to the observed ratio of the corresponding tumour numbers, 53/645; i.e. we can write: tumours in mid-thirds total tumours
0.488 P c +0.103 P T
1.522Pc+1.97lPT _53_ 645
which gives :P c /P T =0.163 ±0.060 (SE).
(3) (4)
where the standard error includes the errors given in Table III and a statistical error on the numbers of tumours scored. The order of accuracy of this value of P C / P T can be established in another way. We can assign various values to PC/PT between 0 (where no
Areas summed
Cortical endosteum (m2)
Trabecular endosteum (m2)
Numbers of tumours
Totals for six long bones Totals for mid-sections
1.522±.022
1.971 ±.040
645
O.488±.OI2
0.103 ±.003
53
068
FIG. 9. Cortical correlation coefficients versus assigned values of PC/PT; the correlation coefficients are for linear regression of numbers of tumours apportioned to cortical bone in individual thirds against the corresponding cortical area.
tumours would occur in the cortex) to 1.0 where the cortical and trabecular surfaces would be equally sensitive. Using any one of these values and the individual values of the cortical and trabecular surface areas, the observed tumour numbers for a bone section can be apportioned between the cortex and the trabeculation of that section. The apportioned numbers for cortical bone can then be tested for correlation with cortical area and the correlation coefficient for linear regression calculated. These correlation coefficients are shown in Fig. 9, plotted against the assigned values of PC/PT- The correlation coefficient shows a maximum at P C / P T ^0.2, thus lending support to the value of PC/PT calculated by Equation (4). DISCUSSION AND CONCLUSIONS
The correlations shown in Table II and in Figs. 2, 4 and 6 suggest that in the case of the human long bones the occurrence of bone tumours shows an approximately linear relationship with trabecular surface area. This is an example that lends some
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quantitative support to the hypothesis that, under given circumstances, tumour induction is proportional to the number of cells at risk (Mayneord and Clarke, 1975). It does not follow that similar correlations can be assumed for other bones in the skeleton; the data given by Thurman et ah, (1973) suggest that this may be difficult, but as yet knowledge of the surface areas involved is not available to examine the question. Among the long bones themselves there are some discrepencies in that, for the natural tumours, more occur in the distal femur and less in the proximal femur than the regression lines suggest, whereas the corresponding points for the radium-case data fit quite well. The slopes of the regression lines are also somewhat different for the two sets of natural tumour data and both differ from that obtained for the radium cases. Nevertheless there is still a strong suggestion of a relationship between the frequency of occurrence at a given site and the associated surface area. As to other possible factors that might influence the location of bone tumours, there appear to be no data reported on variation with age or sex. The known greater proliferative capacity of cells near trabecular surfaces presumably underlies the greater rate of bone turnover in trabecular compared with cortical bone, and our results are in accord with this. With regard to the radium-case data, the analyses against skeletal dose have been examined as far as present data will allow. The two main features of the dose data are (a) the great diversity of dose among the cases examined and (b) the very high doses sustained in the majority of the cases. Under these circumstances it is evident that area of surface at risk is a stronger factor than dose in influencing the site of tumour appearance. Assuming, however, that radiation is the causative agent in these radium cases, a very approximate estimate can be made of the sarcoma risk per unit area of endosteal surface under conditions of very high skeletal dose. If the 33 longbone sarcomas listed in Table I are taken as occurring in the 777 cases analysed by Rowland et al. (1970), the risk per unit area of trabecular surface is about 2 X 10~6 cm"2 over a period of 40 to 50 years of observation, the risk to surfaces in cortical bone being about six times lower. If the cells at risk lie within about 10 /xm of the surfaces, the probability of tumour occurrence in the trabeculation of the long bones would thus be about 2 X 10~9 per g of cells. These estimates can only be approximate because the tracing of radium cases is incomplete. Considering all the data together it has been possible to derive a value for the relative probability
of tumour occurrence per unit area of cortical and trabecular endosteum. The value obtained gives a quantitative figure which supports the qualitative expectations based on biological considerations and the practical observation that comparatively few tumours appear in the mid thirds of the long bones. A value of P C / P T = 0 . 1 6 is suggested as a reasonable value to use in any dosimetric calculation of carcinogenic risk to cortical bone surfaces compared with that to trabecular surfaces. ACKNO WLEDGMENTS
We are greatly indebted to many people with whom we have discussed various aspects of this work, particularly in the early stages with Dr. C. W. Mays of the University of Utah and Dr. J. H. Marshall of the Argonne National Laboratory and later with Dame Janet Vaughan, Sir Edward Pochin and Professor W. V. Mayneord. Our thanks are also due to Drs. R. E. Rowland and A. T. Keane of the Argonne National Laboratory for data on the radium cases. We gratefully acknowledge the help of Dr. W. K. J. Walls of the Department of Anatomy, Leeds University and the technical help of Miss Barbara Prestwich. The work was supported by the Medical Research Council. REFERENCES ATKINSON, P. J., 1965. Changes in resorption spaces in femoral cortical bone with age. Journal of Pathology and Bacteriology, 89,173-178. BEDDOE, A. H., 1977. Measurements of the microscopic structure of cortical bone. Physics in Medicine and Biologv, 22, 298-308. BEDDOE, A. H., DARLEY, P. J., and SPIERS, F. W., 1976.
Measurements of trabecular bone structure in man. Physics in Medicine and Biology, 21, 589-607. DARLEY, P. J., 1968. Measurement of linear path length distributions in bone and bone marrow using a scanning technique. In Proceedings of a Symposium on Microdosimetry, Ispra, Italy, E.A.E.C. Report E.U.R. d-f-e-, pp.509-526. International Commission on Radiological Protection, 1968. A Review of the radiosensitivity of the tissues in bone. I.C.R.P. Publication No. 11 (Pergamon Press, Oxford). LLOYD, E., ROWLAND, R. E., HODGES, D., and MARSHALL,
J. H., 1967. Surface/volume ratios of bone determined by computer analysis of micro-radiographs. Argonne National Laboratory, Radiological Physics Division Report ANL7360, pp. 93-96. MAYNEORD, W. V., and CLARKE, R. H., 1975. Carcinogenesis
and radiation risk. A biomathematical reconnaissance. British Journal of Radiology, Supplement 12, Chapter 1. ROWLAND, R. E., FAILLA, P. M., KEANE, A. T., and STEHNEY
A. F., 1970. Some dose-response relationships for tumour incidence in radium patients. Argonne National Laboratory Report ANL-7760II, pp. 1-17. ROWLAND, R. E., and KEANE, A. T., 1976. Personal com-
munication. SISSONS, H. A., 1970. Dimensions of cells covering bone surfaces. Medical Research Council (London) SubCommittee on Permissible Levels, PIRC/PL/70/4. THURMAN, G. B., MAYS, C. W., TAYLOR, S. N., KEANE,
A. T., and SISSONS, H. A., 1973. Skeletal location of radiation-induced and naturally occurring osteosarcomas in man and dog. Cancer Research, 33,1604—1607. VAUGHAN, J., 1970. Note on character of cells on trabecular bone surfaces in adult human vertebrae. Medical Research Council (London) Sub-Committee on Permissible Levels, PIRC/PL/ 70/1.
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